Analysis of a nonoverlapping domain decomposition method for elliptic partial differential equations

In this study we analyze a nonoverlapping domain decomposition method for the solution of elliptic Partial Differential Equation (PDE) problems. This domain decomposition method involves the solution of Dirichlet and Neumann PDE problems on each subdomain, coupled with smoothing operations on the interfaces of the subdomains. The convergence analysis of the method at the differential equation level is presented. The numerical results confirm the theoretical ones and exhibit the computational efficiency of the method.